Cloud Making in the Laboratory Condensation Nuclei

Aitken (1923)'s method was to expand suddenly a closed volume of air standing over a water surface containing saturated water vapour into a larger volume. This is not exactly what happens in Nature, for when air saturated with water vapour goes up, say to a height of 2 km, the pressure falls and the mass of air expands gradually in volume and the expansion is not large. In the laboratory experiment, the expansion is sudden, and generally large.

However, in the atmosphere as well as in the laboratory process, the temperature falls and the air becomes super-saturated, i.e., it contains more water vapour than it can normally do and the excess amount of vapour is expected to be condensed in the form of small water droplets forming a fog-like cloud. This was actually found to be the case in the laboratory experiment; but what surprised Aitken and other physicists was the fact that if expansion was done with the same airmass in a limited volume, a number of times, then after a few expansions no fog would be formed even though these expansions were quite sufficient for producing supersaturation.

This was traced to the surprising fact that dust-particles which are normally present in the air are actually essential for the formation of a fog or cloud. In fact, if the expansion experiments are carried out from the very start with dust-free air, such as is obtained by sucking air through glass wool, no fog would be formed even at the first expansion. In the experiments of Aitken, ordinary air was taken which contains enough dust particles. After a few expansions, these are all precipitated. The air becomes dust-free and no further fogs are formed after expansion. The explanation of this surprising fact was speedily forthcoming.

Lord Kelvin (1870) had shown from thermodynamical considerations that the saturation vapour pressure of liquids over a curved surface, such as that of a small drop, of radius 'r', was considerably higher than that over a plane surface on account of the surface tension of liquids. The relation (a theoretical derivation of this relation is presented in Appendix-5) is ln(er/es) = (2 o/r)/(nkT) (5.2.1)

where er and es are the saturated vapour pressures over the curved surface and the plane surface respectively, o is the surface tension of water, n is the number of molecules per unit volume, k is Boltzmann constant and T is the temperature in degrees Absolute.

For a water drop at 10 °C, the values of (er/es) calculated from the above formula for different dropsizes are given in Table 5.1.

Table 5.1 emphasizes the need of existence of nuclei of condensation. The H2O-molecule has a radius of 2 x 10~8cm. Ordinarily,in the process of cooling, nearly 100 molecules of water must come together if they were to form a tiny droplet of radius ~ 10~7cm. But this would not be stable, as the above figures show unless the degree of supersaturation exceeds 3.1, i.e., the cooled atmosphere contains three times more water vapour than is given by the saturation vapour pressure curve (Fig. 4.3). In the absence of such supersaturation, the drop evaporates as soon as it is formed. But if a dust particle having a radius of 10~6 cm is present, water molecules depositing on it form a droplet of radius of 10~6cm and now the supersaturation needed is only 1.12 which is generally to be found in cooled air. So, droplets formed by deposition of water molecules on dust particles will continue to grow. The laboratory experiments prove that some kind of nuclei must exist if cooled water vapour is to form fogs or clouds under atmospheric conditions.

Table 5.1 Values of er/es for drops of water r (cm) 2 x 10~8 10~7 10~6 10~5 10~4

5.3 Atmospheric Nuclei - Cloud Formation in the Atmosphere

What are actually the nuclei on which clouds form in the atmosphere?

Dust is a very vague term which denotes minute particles of earth consisting mostly of sand or quartz carried upward by wind. In addition, there may be other types of particles which may act as nuclei for condensation. These are particles constituting smoke from industrial cities, particles of salt, like sodium chloride and magnesium chloride which are carried by wind over sea surfaces in the form of spray; these evaporating in the atmosphere, leave nuclei of minute particles of salt. There may be, in addition, particles composed of oxides of nitrogen or SO3, which are formed by the action of sunlight on nitrogen and oxygen molecules, or on sulphur nuclei which are found to exist in industrial areas.

Some of these nuclei are hygroscopic, i.e., can easily draw water to them. The supersaturation needed for formation of drops on these hygroscopic nuclei is much smaller than on dust nuclei. In fact, laboratory experiments show that hygroscopic particles can gather moisture round them at relative humidities much below 100%. Owens in1926 in a paper in the Proceedings of the Royal Society of London described occasions when nuclei began to draw moisture at a relative humidity of 74%. How do particles grow under such conditions? The earliest experiments carried out to answer this question were those of Kohler (1926) and the trend of his results is shown in Fig. 5.1.

The curve in Fig. 5.1 serves to show that condensation increases with rise of relative humidity slowly at first, but very rapidly when the relative humidity approaches 100%, or exceeds this value. It is natural to ask at this stage to what extent condensation can proceed on hygroscopic nuclei and what will be the order of the size of a drop formed in this way. From our previous considerations we can try an answer to this question. In the initial stages of absorption of water vapour the saturation vapour pressure on the surface of the drop decreases with increase of size, but at the same time the reduction of the salt concentration causes a rise in the saturation vapour pressure. Thus two opposing forces come into play at the surface of the growing nucleus and further condensation stops when they balance each other. The maximum size of a droplet formed in this way has been estimated to be of the order of 10"4 to 10"3 cm in radius which is usually the order of size of an atmospheric fog or cloud droplet.

Fig. 5.1 Size of condensation nuclei at different relative humidities (After Kohler, 1926)

Fig. 5.1 Size of condensation nuclei at different relative humidities (After Kohler, 1926)

There is yet another factor which we have to consider while studying the physics of drop formation. It is the effect of electric charge on the condensation of vapour on a drop. J.J. Thomson showed that if a drop contains an electric charge 'E', the saturation vapour pressure on its surface is reduced. The relation is given by ln(er/es) = {(2 o/r) - (E2/8nr4)}/(nkT) (5.3.1)

where the symbols have the same meanings as in (5.2.1). If we put the right-hand side of (5.3.1) equal to zero, it is easy to show that for every value of the radius there is what is called a critical charge which will make er = es, i.e., it will reduce the saturated vapour pressure over the drop to that over a plane surface. The value of the critical charge calculated for different drop sizes is given in Table 5.2.

C.T.R. Wilson in 1897 using his cloud chamber demonstrated the role of electrically charged particles in the formation of condensation nuclei in a supersaturated atmosphere. He sent a high-energy charged particle like a-ray from radium through a supersaturated vapour and by strongly illuminating the chamber photographed the track of the a-ray inside the chamber. This could be done because in passing through the gases inside the chamber the a-ray owing to its tremendous energy knocked off electrons from the gaseous molecules and it was these electrons which because of their electric charge rapidly gathered moisture round them and formed the minute droplets which constituted the path of the a-ray under strong illumination. Because of high electronic density, the saturation vapour pressure on the ions initially formed was considerably reduced and thus the supersaturation prevailing inside the chamber was sufficient to produce rapid condensation on them to form the visible drops.

What is the order of electronic charges that can aid rapid condensation on atmospheric nuclei? According to Table 5.2, the critical charge for a drop of radius 10-6cm, which is the order of the size of average nuclei in the atmosphere, is as large as 130. Multiple electronic charges of this high order are seldom met with in the atmosphere. There is evidence of multiple electronic charges on fog droplets and rain drops but the charge on atmospheric nuclei, at least in the early stages of condensation, seldom exceeds one electronic charge. It is, therefore, rather unlikely that the effect of electric charge plays any important part in the formation of cloud drops in the atmosphere.

It is, therefore, recognized that some kind of 'nuclei' is necessary for the condensation of water vapour into droplets which composes a cloud, but which kind of nuclei - quartz particles (dust), Na Cl crystals obtained from sea-spray, or nitrous crystals play the predominant part is not yet decisively known. It is, however, found that only a small and variable fraction of the total number of particles that are measured in the continental and marine air act as cloud condensation nuclei. Observations made over the various parts of the globe do not suggest any systematic

Table 5.2 Critical electric charges for drops r (cm) 4 x 10-8 2 x 10-7 4 x 10-6 9 x 10-5 2 x 10-3 4 x 10-2 E (charge) 1 10 1 03 1 05 1 07 109

Fig. 5.2 Concentration of Cloud condensation nuclei (CCN) in continental and marine air near surface at different supersaturation (After Twomey and Wojciechowski, 1969, with permission of American Meteorological Society)

Fig. 5.2 Concentration of Cloud condensation nuclei (CCN) in continental and marine air near surface at different supersaturation (After Twomey and Wojciechowski, 1969, with permission of American Meteorological Society)


variations in the concentration of cloud condensation nuclei (CCN) with latitude or seasons. However, observations taken near the earth's surface show that the average concentration of CCN is much higher over continents than over oceans, as revealed by Fig. 5.2 reproduced from Twomey and Wojciechowski (1969).

However, the concentration of CCN over the land is found to fall off with height by a factor of about 5 between the surface and 5 km, whereas that over the ocean remains more or less constant with height. There also appears to be a diurnal variation in the concentration of CCN near the surface with a minimum in the morning and maximum in the evening.

5.4 Drop-Size Distribution in Clouds

Further elucidation of the problem depends upon our knowledge of the size of droplets forming clouds, and the actual size and nature of the nuclei on which these droplets are formed. 'Clouds' denote a wide variety of types, from low-lying fogs or stratus clouds which seldom give any precipitation to heavy rain-clouds enormous in extent and yielding large precipitation. Meteorologists have invented a system of classification which has been accepted by the International Meteorological Committee and is published in the International Cloud Atlas. The classification depends mostly on external physical appearance, levels of formation in the atmosphere (e.g., low, medium or high) and composition (whether they are made up of water droplets, or ice particles, or a mixture of both).

The point we have to discuss is why some clouds vanish without giving rain, while others give copious precipitation. This is answered by a close study of the distribution of droplet sizes in clouds.

Fig. 5.3 Drop-size distribution in fog and low stratus clouds (Reproduced from G.F. Taylor, Aeronautical Meteorology, 1941, p 261)

Fig. 5.3 Drop-size distribution in fog and low stratus clouds (Reproduced from G.F. Taylor, Aeronautical Meteorology, 1941, p 261)

Diameter Cd) in Microns

Courtesy H. G. Houghton

Diameter Cd) in Microns

Courtesy H. G. Houghton

Measurements have been made of the size of droplets in clouds by aeroplane ascents and other methods. They are found to range in radius from 10 to about 60 microns (1micron = 10"4 cm, usually denoted by the symbol with a mean value of about 20 in a fog or low-lying stratus cloud.

Figure 5.3, originally due to H.G. Houghton, shows the distribution of sizes of drops in a low-lying fog, as presented by Taylor (1941).

The droplets which are precipitated as rain have much larger radii. They range in value from 100 ^ to 1/4 of a centimetre. Drops larger than these generally get broken by air during the fall. Thus the difference between clouds that hover and disappear without giving any rain and those which give rain is, therefore, entirely one of the dimension of the drops of which they are composed, the hovering clouds consisting of droplets less than 100 microns in diameter, and the rain-giving clouds consisting of larger drops. We can understand the cause of this differential behaviour of the particles with the aid of the well-known Stokes'law which deals with the rate of fall of small particles through a viscous fluid, such as the air.

5.5 Rate of Fall of Cloud and Rain Drops

As soon as a drop is formed, it begins to fall, under gravity, but its fall is resisted by the viscous drag of the air. According to Stokes' law, the rate of fall of a very small particle of radius 'r' and density p through a fluid of density •, which is called the terminal velocity, is given by v = 2g r2 (p - -)/9 V

Table 5.3 Particle sizes and their velocity and distance of fall

Size of particles

Velocity of fall

Time of fall

Diameter (|)

(cm s"1)

through 1 km


4 x 10"4



Ions and nuclei

(1-100) x 10"3



Cloud particles


(5 x 10"2-1.3 x 100)

21 hour




20 minutes (m)

Light rain



8 minutes

Heavy rain

(1.5-2.0) x 103


3 minutes

Cloud burst

3.0 x 103


2.4 minutes

Largest raindrop

5.0 x 103


2 minutes

where v denotes the velocity, g is acceleration due to gravity and | is molecular viscosity of the fluid.

For a cloud droplet of about 10| in radius, the terminal velocity, as calculated from (5.5.1) is 1.3cms_1 and it takes about 21 h to fall through a height of 1 km. It, therefore, evaporates before it reaches the ground. The smaller the particle, the more slowly it falls, and, therefore, more quickly it evaporates.

Table 5.3, adapted from a paper by Simpson (1941), makes these points clear. It shows that the largest raindrop that falls through the air at a velocity of 8 ms"1 has a diameter of 5 mm. It falls through a height of 1 km in about 2 min.

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  • monica
    Why charged particles aid condensation?
    9 years ago
    What happens when earths atmosphere is saturated with water vapor?
    9 years ago

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